Further Developments of the Pluripotential Theory (Survey)

Abstract

It is well known that pluripotential theory, constructed in the 1980s, is based on plurisubharmonic (psh) functions and on the Monge-Amp\(\grave{e}\)re operator \((dd^c u)^n\). In the 1990s there were many attempts to develop and expand pluripotential theory to broader classes such as the class of m-subharmonic \((m-sh)\) functions \((1\le m \le n)\). In this paper we will discuss some of the most important results of the theory of \(m-sh\) function as well as the difficulties and problems of constructing a potential theory in the class of \(m-sh\) functions.

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